Double-crystal Diffractometer Research Articles

Small angle scattering signals for (neutron) computerized tomography

Small angle neutron scattering is a well-established tool for the determination of microscopic structures in various materials. With the ultrasmall angle neutron scattering technique (USANS), structures with sizes of approximately 50nm to 50μm can be resolved by a double crystal diffractometer (DCD). USANS signals recorded with a special DCD were used for tomographic purposes investigating the macroscopic structure of a sample with a maximum resolution of 200μm. Thereby, macroscopic regions within the sample with different ultrasmall angle scattering properties, i.e., with different microscopic structures, could be imaged by the means of tomographic reconstruction from projections (on a macroscopic scale).

Application of ultrasound for the simultaneous improvement intensity and resolution of the Bonse–Hart diffractometer

It is calculated that simultaneous ultrasonic excitation of the Bonse–Hart monochromator and analyzer leads to the improvement of resolution and increasing of the intensity. It is argued that incoherent ultrasonic field is applicable in similar experiments. Ultrasonic phonon satellites were studied by means of Bonse–Hart channel cut crystal. Strong improvement of contrast with moderate loss of intensity was observed in this case. Double Crystal diffractometer with ultrasonically excited monochromator and analyzer was applied for the ultrasonic phonon satellite research. It was observed for the first time that this “double sound” technique leads to the strong improvement of contrast and simultaneously 60% increasing of the intensity.

Neutron tomography in double crystal diffractometers

Using a double crystal diffractometer (DCD) for tomographic imaging introduces the possibility to use various signals for image contrast. In conventional neutron and X-ray radiography and tomography the contrast signal for imaging arises just from the attenuation in the sample. Due to recent developments in digital imaging tomography gained a lot of importance in medicine and non-destructive testing (NDT). But not all materials deliver an useful contrast concerning attenuation neither in the case of X-rays nor for neutrons. In a DCD attenuation but also other interactions between penetrating radiation and sample can be registered. Besides the common attenuation there are especially refraction and small-angle scattering effects. It will be shown at least for neutrons that from each of these signals recorded as tomographic projections in a DCD an image of the sample can be reconstructed by the means of common filtered back projection (FBP) algorithm. Additionally, all the signals can be registered in one measurement and can be used for independent reconstructions resulting in different images expressing different characteristics of the sample.

Direct comparison of plastically deformed Ge mosaic crystal and bent perfect Si crystal for neutron monochromatization

The results of direct comparison of some monochromator properties of plastically deformed (mosaic) Ge single crystal with cylindrically bent perfect crystal (BPC) of Si are presented. Using a double-crystal diffractometer and α o=20′ collimation of the incident polychromatic beam we compared monochromatic beam current at the sample position for the take off angles of 40°, 50° and 60°. The comparison was carried out on the diffraction planes (3 1 1) M when the monochromators operated at nearly the same asymmetric diffraction geometry. For the sake of comparison of their resolution properties, Fe(1 1 0) and Fe(2 1 1) diffraction profiles of the beam scattered by a solid and well annealed α-Fe polycrystalline sample are also presented. It has been found that under these specific experimental conditions often used for residual strain scanning, the focusing bent Si crystal is a good cheap alternative to the flat mosaic Ge monochromator.

First realisation of a three-dimensional refraction contrast computerised neutron tomography

We performed tomographic investigations of a sample with a special double crystal diffractometer (DCD) using only the refraction of a neutron beam as imaging signal. Up to now refraction contrast tomographies with DCDs have been performed with the standard detectors and linear position sensitive detectors (PSD). Especially the combination of a bent crystal type DCD with a PSD saved exposure time and increased the accuracy of the reconstructed image. However, the reconstructed objects had to be (high) slices of an object (having congruent cross sections in the height) due to the lack of any vertical resolution. Hence only two-dimensional slices of samples could be reconstructed and imaged. As the refraction effect is measured in a horizontal plane of scattering, other refraction angles out of that plane of scattering could be neglected. Therefore, a three-dimensional reconstruction of the sample volume becomes possible with a two-dimensional position sensitive detector. First results achieved by this set-up using the refraction contrast method will be given.

Fine-rotation attachment to standard goniometers

A new type of fine-rotation stage has been constructed and tested. It can be attached to standard goniometers used in X-ray and neutron crystallography. The device consists of a shaft and a bar that is fitted tightly to a hole traversing the shaft. The diameter of the shaft is 5 to 10 times larger than the diameter of the bar and the length of the bar is about 5 times larger than the height of the shaft. The bottom of the shaft is attached to the top plate of the goniometer and a goniometer head can be fitted to the other end of the shaft. The free end of the bar is pushed tangentially by a linear actuator to produce a torsion moment at the shaft. The dimensions and materials of the prototype were chosen such that a 1 mm bend of the bar corresponded to a torsion angle of the shaft of about 20 µrad. The rotation angle was measured using a double-crystal diffractometer in the non-dispersive setting, with MoKα1radiation from a fine-focus X-ray tube. Accurately known angular deviations were produced by refraction in a prism and the shifts in the rocking-curve position were measured. The measured torsion angle agreed within 4% with the value calculated from the elastic constants and dimensions of the device. The repeatability of the angle was ±20 nrad (0.004 arcsec).

USANS investigation of early stages of metal foam formation

Metallic foams are on the verge of being used in industrial applications. However, the mechanism of foam creation, especially the early stages, are still unexplored. Ultra small-angle neutron scattering (USANS), performed with the double-crystal diffractometer (DCD) at the Geesthacht Neutron Facility (GeNF), is a promising method for obtaining a three-dimensional average of a pore size distribution in a wide size range from about 100 nm to about 20 μm. Analysis of the neutron scattering curves yielded pore size distributions which conformed with the results obtained by microscopy.

Thermal neutron optical experiments with tuneable many-bounce channel-cut crystals

We realized the first tuneable channel-cut crystals to be used as monochromator and analyzer in a double-crystal diffractometer and demonstrated the superior operation for ultra small angle scattering. With this new system it was possible to measure the ultra small angle scattering from a single 14-μm glass fibre, the small angle scattering from an Al wedge and the diffraction pattern of a Si phase grating. The last measurement was only possible due to the reduction of the Darwin width of both crystals from 5.7 sec of arc (natural Darwin width) to 1.4 sec of arc.

First realization of Bonse-Hart angular profiles for multiple Bragg reflections

We have produced a monochromatic neutron beam with the sharpest yet angular profile. We evolved an optimal design for the geometry of a channel-cut perfect crystal effecting a multiple Bragg reflection. Using a pair of such channel-cut silicon crystals, we recorded rocking curves for a triple-triple symmetric {111} Bragg reflection of 5.229 A neutrons at the V12b Double Crystal Diffractometer in BENSC. The data agree with the theoretical Darwin reflection curves over an intensity range spanning five orders of magnitude. This constitutes the first realization of the proposal made by Bonse and Hart 35 years ago. Our results mark an order of magnitude improvement over the previous best USANS profiles.

Characterisation of creep cavitation damage in a stainless steel pressure vessel using small angle neutron scattering

Grain-boundary cavitation is the dominant failure mode associated with initiation of reheat cracking, which has been widely observed in austenitic stainless steel pressure vessels operating at temperatures within the creep range (>450 °C). Small angle neutron scattering (SANS) experiments at the LLB PAXE instrument (Saclay) and the V12 double-crystal diffractometer of the HMI-BENSC facility (Berlin) are used to characterise cavitation damage (in the size range R=10-2000 nm) in a variety of creep specimens extracted from ex-service plant. Factors that affect the evolution of cavities and the cavity-size distribution are discussed. The results demonstrate that SANS techniques have the potential to quantify the development of creep damage in type-316H stainless steel, and thereby link microstructural damage with ductility-exhaustion models of reheat cracking.

Observation of edge refraction in ultra small angle neutron scattering

Slits and macroscopic objects such as edges give rise to refraction and diffraction. In this Letter we show the effect of Cd edges and slits if they are inserted between the monochromator and analyser in a double crystal diffractometer. Despite to the use of wavelengths of tens of nanometer and strong absorbing materials refraction is observed which contributes to enhanced wing intensity of the instrumental curve of the double crystal diffractometer.

Observation of Edge Diffraction with a Double Crystal Diffractometer

We have observed edge diffraction with a double crystal diffractometer and therefore can explain the enhanced wing intensity of measured Darwin profiles in dynamical diffraction. Precise experiments uniquely demonstrate the contribution of Fresnel diffraction at absorbing straight edges, interpreted as ultra small angle scattering (USAS) or diffuse scattering in other experiments. No contributions were found due to ultra small surface scattering or TDS stemming from the crystals, which was proposed by other groups to explain the enhanced wing intensity of their measured rocking curves.

An x-ray rocking curve technique for the absolute characterization of epitaxial layers and single-crystal solids

A rapid double-crystal x-ray diffractometer technique for the absolute measurement of lattice parameters in single crystals and epitaxial layers is introduced. The method is based on the principle that in a diffractometer aligned for rocking curve measurements within a given zone, the zero setting correction is the same for all crystal angles within the zone. The peak positions can thus be measured and corrected quickly, and the lattice parameters evaluated within each layer independently of others. The proof-of-principle tests are given for Si and InP, and the method is applied to a GaN film grown on an a-plane sapphire wafer. The method has unlimited accuracy depending only on the instrumental alignment and material quality.

Analysis of neutron double-crystal diffractometer scattering curves including multiple scattering

Double-crystal diffractometers (DCD) of the Bonse–Hart type are used for small-angle neutron scattering (SANS) experiments with very high resolution. Scattering from inhomogeneities in the size range of typically 100 nm to 10 µm can be detected with a DCD. The evaluation of DCD scattering curves is more complicated than for conventional SANS instruments with point collimation for two reasons: first, a DCD operates with a long-slit geometry, and second, owing to the high scattering power of large inhomogeneities, multiple small-angle scattering is likely to play a significant role in many DCD experiments. A numerical procedure is proposed for the determination of particle size distributions from DCD scattering curves influenced by multiple scattering. This procedure is based on ann-fold convolution of single-scattering cross sections, wherendepends on the degree of multiple scattering. It makes use of the indirect Fourier transformation method and thus, firstly, size distributions of arbitrary shape can be determined, and secondly, the calculation is fast, allowing an interactive analysis. The procedure is demonstrated with scattering from latex particles with different degrees of multiple scattering. The results show that the size and volume fraction of the latex spheres can be determined with a reasonable error even from scattering curves that are strongly influenced by multiple small-angle scattering.

X-ray study of silicon crystal structure changes due to implantation with fast nitrogen ions

An analysis of X-ray rocking curves and reciprocal space maps recorded for silicon single crystals before and after implantation with a 5×10 14-cm −2 dose of 3 MeV/n nitrogen ions is presented. Silicon single crystals of orientation (100) were obtained by the Czochralski method. X-ray investigations were performed by means of a high-resolution Philips diffractometer using the characteristic Cu Kα 1 radiation, and the integral reflectivities were measured with a double crystal diffractometer using the characteristic Ag Kα 1 radiation. It was stated that irradiation with fast nitrogen ions can create extended defects as well as formation of nano-areas of disordered structure in the silicon crystal. An increase in the surface roughness was also determined from the grazing incidence X-ray reflectivity measurements.

X-Ray diffraction determination of the fractions of hexagonal and twinned phases in cubic GaN layers grown on (001)GaAs substrate

Being an established qualitative method for investigating presence of additional phases in single crystal materials, X-ray diffraction has been used widely to characterize their structural qualities and to improve the preparation techniques. Here quantitative X-ray diffraction analysis is described which takes into account diffraction geometry and multiplicity factors. Using double-crystal X-ray four-circle diffractometer, pole figures of cubic (002), {111} and hexagonal {101̄0} and reciprocal space mapping were measured to investigate the structural characters of mixed phases and to obtain their diffraction geometry and multiplicity factors. The fractions of cubic twins and hexagonal inclusions were calculated by the integrated intensities of rocking curves of cubic (002), cubic twin {111}, hexagonal {101̄0} and hexagonal {101̄1}. Without multiplicity factors, the calculated results are portions of mixed phases in only one {111} plane of cubic GaN. Diffraction geometry factor can eliminate the effects of ω and χ angles on the irradiated surface areas for different scattered planes.

Experimental characterization of bent focusing crystals

It has been established with the aid of a double-crystal X-ray diffractometer that the nonuniform curvature of cylindrically, spherically, or thoroidally bent silicon and quartz crystals is of a periodic character. It is shown that this periodicity influences the spectral (energy) resolution of a focusing crystal, which becomes noticeable at the Bragg angle θ obeying the condition tan2 ≫ 1.

Multiplicity factor and diffraction geometry factor for single crystal X-ray diffraction analysis and measurement of phase content in cubic GaN/GaAs(001) epilayers

On the basis of integrated intensity of rocking curves, the multiplicity factor and the diffraction geometry factor for single crystal X-ray diffraction (XRD) analysis were proposed and a general formula for calculating the content of mixed phases was obtained. With a multifunction four-circle X-ray double-crystal diffractometer, pole figures of cubic (002), {111} and hexagonal {1010} and reciprocal space mapping were measured to investigate the distributive character of mixed phases and to obtain their multiplicity factors and diffraction geometry factors. The contents of cubic twins and hexagonal inclusions were calculated by the integrated intensities of rocking curves of cubic (002), cubic twin {111}, hexagonal {1010} and {1011}.

High resolution X-ray diffraction using a high brilliance source, with rapid data analysis by auto-fitting

In a production environment in particular, fast data collection and analysis, which are also highly reliable, are desirable. Measurement can be speeded up by increasing the diffracted intensity, thus reducing the time required to measure it reliably. Increased intensity with a smaller beam footprint at the sample have been achieved in a double-crystal diffractometer by the use of a novel ellipsoidal mirror working by total external reflection, positioned before the reference crystal. To optimise the performance of the mirror and provide high brightnesses, an X-ray source with a very small focal spot is required. Such a high brightness source has been made that uses electromagnetic focusing of the electron beam onto the target. Rapid data analysis is achieved by the use of an auto-fitting program that employs a genetic algorithm and the full dynamical theory of X-ray diffraction. Choice of an appropriate error function produces a deep global minimum while the genetic algorithm avoids convergence on local minima. From the model that produces the best fit, samples parameters such as layer thickness and alloy composition are extracted with quantified goodness of fit.

Performance of a double crystal diffractometer with different channel-cut perfect Si crystals

The double crystal diffractometer (DCD) at the Geesthacht Neutron Facility (GeNF) is equipped with triple-bounce channel-cut perfect Si(111) crystals. In this way the intrinsic background of DCD, i.e. given by the rocking-curve wings, has been decreased dramatically. Its former dependence on the scattering vector q of q −2 was changed to q −6. An observed deviation from the q −6 behaviour is possibly attributed to neutrons propagating and diffracting inside the walls of the channel-cut crystals. In order to reduce this parasitic intensity and for further improvement of DCD with respect to higher sensitivity to weak sample scattering quintuple-bounce side grooved channel-cut crystals have been used. The change in the rocking curves without and with inserting cadmium in the grooves of the walls is pointed out. The efficiency of DCD is shown in the case of neutron scattering from Latex spheres with radii of about 2200 nm.